The linking number and the writhe of uniform random walks and polygons in confined spaces

Panagiotou, E; Millett, KC; Lambropoulou, S

dc.contributor.author	Panagiotou, E	en
dc.contributor.author	Millett, KC	en
dc.contributor.author	Lambropoulou, S	en
dc.date.accessioned	2014-03-01T01:34:46Z
dc.date.available	2014-03-01T01:34:46Z
dc.date.issued	2010	en
dc.identifier.issn	1751-8113	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20847
dc.subject.classification	Physics, Multidisciplinary	en
dc.subject.classification	Physics, Mathematical	en
dc.subject.other	TOPOLOGICAL CONSTRAINTS	en
dc.subject.other	CROSSING NUMBER	en
dc.subject.other	RANDOM KNOTS	en
dc.subject.other	STATISTICAL MECHANICS	en
dc.subject.other	POLYNOMIAL INVARIANT	en
dc.subject.other	SCALING BEHAVIOR	en
dc.subject.other	SUPERCOILED DNA	en
dc.subject.other	TOTAL CURVATURE	en
dc.subject.other	CLOSED CURVES	en
dc.subject.other	TOTAL TORSION	en
dc.title	The linking number and the writhe of uniform random walks and polygons in confined spaces	en
heal.type	journalArticle	en
heal.identifier.primary	10.1088/1751-8113/43/4/045208	en
heal.identifier.secondary	http://dx.doi.org/10.1088/1751-8113/43/4/045208	en
heal.identifier.secondary	045208	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	Random walks and polygons are used to model polymers. In this paper we consider the extension of the writhe, self-linking number and linking number to open chains. We then study the average writhe, self-linking and linking number of random walks and polygons over the space of configurations as a function of their length. We show that the mean squared linking number, the mean squared writhe and the mean squared self-linking number of oriented uniform random walks or polygons of length n, in a convex confined space, are of the form O(n 2). Moreover, for a fixed simple closed curve in a convex confined space, we prove that the mean absolute value of the linking number between this curve and a uniform random walk or polygon of n edges is of the form O(√n. Our numerical studies confirm those results. They also indicate that the mean absolute linking number between any two oriented uniform random walks or polygons, of n edges each, is of the form O(n). Equilateral random walks and polygons are used to model polymers in θ-conditions. We use numerical simulations to investigate how the self-linking and linking number of equilateral random walks scale with their length. © 2010 IOP Publishing Ltd.	en
heal.publisher	IOP PUBLISHING LTD	en
heal.journalName	Journal of Physics A: Mathematical and Theoretical	en
dc.identifier.doi	10.1088/1751-8113/43/4/045208	en
dc.identifier.isi	ISI:000273437500014	en
dc.identifier.volume	43	en
dc.identifier.issue	4	en